Results 1 to 10 of about 421 (93)
On a conjecture concerning total domination subdivision number in graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2021 Let be the total domination number and let be the total domination subdivision number of a graph G with no isolated vertex. In this paper, we show that for some classes of graphs G, which partially solve the conjecture presented by Favaron et al.
S. Kosari +5 more
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Total Roman domination subdivision number in graphs [PDF]
Communications in Combinatorics and Optimization, 2020 A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$.
Jafar Amjad
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Total $k$-rainbow domination subdivision number in graphs [PDF]
Computer Science Journal of Moldova, 2020 A total $k$-rainbow dominating function (T$k$RDF) of $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,\ldots,k\}$ such that (i) for any vertex $v\in V(G)$ with $f(v)=\emptyset$ the condition $\bigcup_{u \in N(v ...
Rana Khoeilar +3 more
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On the total domination subdivision numbers in graphs [PDF]
Open Mathematics, 2010 Abstract A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ t(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt
Sheikholeslami Seyed
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Total Domination Multisubdivision Number of a Graph
Discussiones Mathematicae Graph Theory, 2015 The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G.
Avella-Alaminos Diana +3 more
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Domination parameters of a graph with added vertex [PDF]
Opuscula Mathematica, 2004 Let \(G=(V,E)\) be a graph. A subset \(D\subseteq V\) is a total dominating set of \(G\) if for every vertex \(y\in V\) there is a vertex \(x\in D\) with \(xy\in E\).
Maciej Zwierzchowski
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Disjunctive Total Domination Subdivision Number of Graphs
Fundamenta Informaticae, 2020 A set S subset of V (G) is a disjunctive total dominating set of G if every vertex has a neighbor in S or has at least two vertices in S at distance 2 from it. the disjunctive total domination number is the minimum cardinality of a disjunctive total dominating set in G.
Canan Çiftçi, Vecdi Aytaç
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Total Restrained Domination Subdivision Number for Cartesian Product Graph [PDF]
International Journal of Mathematics and Soft Computing, 2013 In this paper we determine the total restrained dominating set and the total restrained domination subdivision number for Cartesian product graph.
P. Jeyanthi, G. Hemalatha
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A New Bound on the Total Domination Subdivision Number
Graphs and Combinatorics, 2009 A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γt (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number $$sd_{\gamma_{t}}(G)$$is the minimum number of edges that must be ...
Odile Favaron +3 more
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On two conjectures concerning total domination subdivision number in graphs
Journal of Combinatorial Optimization, 2019 A subset S of vertices of a graph G without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number $$\gamma _t(G)$$ is the minimum ...
R. Khoeilar +2 more
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